The actual spatial resolution of analytical techniques based on electron beam excitation such as in a scanning electron microscope is governed by the interaction of the primary high-energy electrons with matter. Elastic and inelastic scattering of these electrons leads to a cascade of subsequent excitations in the material, such as excited atomic shell electrons, plasmons, and hot electron-hole pairs within a generation volume that strongly depends on the energy of the impinging primary electrons. An accurate knowledge about the spatial distribution of generated carriers is necessary to assess the spatial resolution and perform quantitative analyses for measurements of either incoherent cathodoluminescence spectra or images or electron beam induced current maps, which result from the electron-hole pairs after their thermalization. The commonly employed Monte-Carlo simulation programs such as CASINO [1] can describe the scattering cascade very well, but do not include the thermalization process. Therefore, we carried out an experimental determination of the generation volume relevant for cathodoluminescence spectroscopy, comparing the results with those determined by CASINO simulations.

To obtain the lateral distribution of generated carriers for sample temperatures between 10 and 300 K, we utilize cathodoluminescence intensity profiles measured across single quantum wells embedded in thick GaN and GaAs layers. Thin (Al,Ga)N and (Al,Ga)As barriers, respectively, prevent carriers diffusing in the GaN and GaAs layers to reach the quantum well, which would broaden the profiles. The experimental cathodoluminescence profiles are found to be systematically wider than the energy loss distributions calculated by means of CASINO, with the width monotonically increasing with decreasing sample temperature. This effect is observed for both GaN and GaAs and becomes more pronounced for higher acceleration voltages. We discuss this phenomenon in terms of the electron-phonon interaction controlling the energy relaxation of hot carriers and of the non-equilibrium phonon population created by this relaxation process. Finally, we present a phenomenological approach to simulate the carrier generation volume that can be used for the investigation of the temperature dependence of carrier diffusion. Our study shows that the paradigm of a temperature-independent generation volume applicable to all SEM-based techniques needs to be revised.